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Expression of type And

from the theory of proveit.numbers.division

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, IndexedVar, Variable, m, n, w, x, y, z
from proveit.logic import And, InSet, NotEquals
from proveit.numbers import Complex, one, zero
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = And(ExprRange(sub_expr1, InSet(IndexedVar(w, sub_expr1), Complex), one, m), InSet(x, Complex), InSet(y, Complex), ExprRange(sub_expr1, InSet(IndexedVar(z, sub_expr1), Complex), one, n), NotEquals(y, zero))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(w_{1} \in \mathbb{C}\right) \land  \left(w_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(w_{m} \in \mathbb{C}\right) \land \left(x \in \mathbb{C}\right) \land \left(y \in \mathbb{C}\right)\land \left(z_{1} \in \mathbb{C}\right) \land  \left(z_{2} \in \mathbb{C}\right) \land  \ldots \land  \left(z_{n} \in \mathbb{C}\right) \land \left(y \neq 0\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4, 5, 6, 7
3ExprRangelambda_map: 8
start_index: 13
end_index: 9
4Operationoperator: 23
operands: 10
5Operationoperator: 23
operands: 11
6ExprRangelambda_map: 12
start_index: 13
end_index: 14
7Operationoperator: 15
operands: 16
8Lambdaparameter: 31
body: 17
9Variable
10ExprTuple18, 27
11ExprTuple20, 27
12Lambdaparameter: 31
body: 19
13Literal
14Variable
15Literal
16ExprTuple20, 21
17Operationoperator: 23
operands: 22
18Variable
19Operationoperator: 23
operands: 24
20Variable
21Literal
22ExprTuple25, 27
23Literal
24ExprTuple26, 27
25IndexedVarvariable: 28
index: 31
26IndexedVarvariable: 29
index: 31
27Literal
28Variable
29Variable
30ExprTuple31
31Variable